If you pass E, you should raise EM and EN to AB and BC respectively. Because BE is the bisector, then EM=EN.

P is the midpoint of EF and PP2 is parallel to EM, so PP2=EM/2=EN/2.

Similarly, PP3=FL/2(L is the vertical foot of F towards BC).

FL, PP 1, EN meet the conclusion of figure 14. 1, EP/PF= 1, where: PP1= (1* fl+1*.

So: PP 1=PP2+PP3.

The second question:

Let FP/PE=m/n

If the first question is auxiliary line, there are: pp2/en = m/(m+n); PP3/FL=n/(m+n)

PP 1 =(m * EN+n * FL)/(m+n)=(PP2 *(m+n)+PP3 *(m+n))/(m+n)= PP2+PP3

In addition, if we don't know the midline theorem of triangle or the proportional relationship of parallel lines in triangle, we can consider the limit case of graph 14. 1, that is, when b=0, BC coincides and the trapezoid becomes a triangle, then MN=AD*n/(m+n), which can be used to prove PP2/en = m/(m+.